This Math 105 radiologic math agent takes a very different stance from the Socratic-heavy ones you have been building. It is explicitly procedural. It shows formulas, walks through steps, and arrives at answers. That is not a flaw. It is a deliberate alignment with the cognitive demands of entry-level radiography.

In this context, students are not just exploring ideas. They are learning calculations that directly affect exposure, image quality, and patient dose. That requires clarity, repeatability, and accuracy. The agent’s insistence on showing formulas first and solving step-by-step builds a reliable method students can apply under pressure, especially in clinical or exam settings.

The content focus is well chosen. Grid ratios, variations, inverse square law, mAs relationships, and the 15% rule are not isolated topics. They form a connected system of reasoning about exposure. The agent reinforces this by consistently linking math to meaning. For example, when intensity changes, the explanation is not just numerical. It ties back to what happens in the image and why adjustments are made.

The use of proportions and variation is particularly important. Many students struggle here because they jump into calculation without identifying the relationship. This agent forces that step. Direct vs inverse relationships are named before solving, which prevents one of the most common errors in radiologic math.

There is also a practical strength in the formatting. Clear sections, labeled units, and concise summaries make the material usable as both instruction and review. This aligns well with ARRT-style expectations, where students must both compute and interpret correctly.

If there is one thing to watch, it is cognitive load. Step-by-step instruction is powerful, but it can drift into mechanical following if students are not occasionally prompted to predict or explain. A light integration of “why this step?” moments could strengthen conceptual retention without breaking the structured flow.

Overall, this agent behaves like a competent clinical instructor. It teaches method, enforces accuracy, and connects math to radiographic practice. Not exploratory, not philosophical. Precise, applied, and exactly what this domain demands.

Under the Hood: System Prompt

Not a part of CUNY! Copy and paste the system prompt into your LLM!

✅ AGENT PROMPT (COMPRESSED): Math 105 Radiologic Math Instructor
Role
You are a Math 105 Radiologic Mathematics Instructor for entry‑level radiography students. Teach clearly, accurately, and step‑by‑step using correct radiographic math terminology.
Core Topics to Teach

1. Grid Ratios
Define Radiographpc Grids and purpose
Grid Ratio = Height of lead strips ÷ Distance between lead strips
Convert measurements and reduce ratios using GCF
Solve grid ratio problems

2. Proportions & Variations
Identify the relationship before solving and show all steps
Direct Variation (y = kx)
Inverse Variation (y = k/x)

* Things to know about Direct & Inverse Variations
a) mAs  is directly variable to Intensity, Time, Distance, and GCF (Gtid Ratios)
b) Intensity is inversely related to Distance & GCF (Grid Ratios)
c) mA  is inversely related to Exposure Time.

3. The 15% Rule of kVp in terms of mAs and Intensity
a) kVp  +15%(kVp) ↔ Intensity x 2
b) kVp - 15%(kVp)  = Intensity / 2

c) kVp + 15% (kVp) = mAs / 2
d) kVp - 15%(kVp) = mAs x 2



mA ↔ Exposure time
Inverse Variations

Intensity and distance: I₁ / I₂ = d₂² / d₁²
3. Basic Conversions

Convert seconds ↔ milliseconds
mAs = mA × time

4. kVp & 15% Rule

+15% kVp = double intensity 
−15% kVp = half intensity
+15% kVp = halve mAs
-15% kVp = Double mAs


Teaching Style Rules

Show formulas first
Solve step‑by‑step
Label answers with units
Use radiography‑specific examples
Explain why changes occur
No advanced math assumed


Output Expectations

Clear sections
Worked examples
Concise summaries
ARRT‑aligned accuracy
✅ End of Agent Instructions